Обучение чтению литературы на английском языке по специальности «Прикладная математика»

Московский государственный технический университет 
имени Н.Э. Баумана 

О.Д. Дикова, Е.А. Юдачева 

Обучение чтению литературы  
на английском языке  
по специальности  
«Прикладная математика» 

Учебное пособие 
 
 
 
 
 
 
 
 
 
 

 

УДК 802.0 
ББК 81.2 Англ-923 
        Д45 

Издание доступно в электронном виде на портале ebooks.bmstu.ru 
по адресу: http://ebooks.bmstu.ru/catalog/238/book1233.html 

Факультет «Лингвистика» 
Кафедра «Английский язык  
для приборостроительных специальностей» 

Рекомендовано Редакционно-издательским советом 
МГТУ им. Н.Э. Баумана в качестве учебного пособия 
 
Дикова, О. Д. 
Обучение чтению литературы на английском языке по 
специальности «Прикладная математика» : учебное пособие / 
О. Д. Дикова, Е. А. Юдачева. — Москва : Издательство 
МГТУ им. Н. Э. Баумана, 2015. — 47, [1] с. 
ISBN 978-5-7038-4198-3  
Учебное пособие состоит из трех уроков и содержит современные неадаптированные тексты, заимствованные из оригинальных источников, о сущности прикладной математики как науки  
и ее связях с другими науками. Каждый из уроков включает базовый текст А, упражнения на контроль понимания текстов, подбор 
активной лексики, перевод с русского на английский язык, умение 
читать математические формулы, а также дополнительные тексты 
для различных видов работ с ними. Грамматические упражнения 
стимулируют повторение наиболее сложных грамматических конструкций. В Приложении приведен перечень основных математических символов и формул, а также даны варианты правильного 
их прочтения на английском языке.  
Для студентов старших курсов факультета «Фундаментальные 
науки», обучающихся по специальности «Прикладная математика». 
 
 
УДК 802.0 
ББК 81.2 Англ-923 

  МГТУ им. Н.Э. Баумана, 2015 
 
  Оформление. Издательство  
ISBN 978-5-7038-4198-3 
МГТУ им. Н.Э. Баумана, 2015 

Д45 

ПРЕДИСЛОВИЕ 

Целью учебного пособия является развитие у студентов старших курсов, обучающихся по специальности «Прикладная математика», навыков работы с оригинальной научной литературой на 
английском языке, а также точного понимания и грамотного перевода текстов, ведения беседы по основным темам, затронутым  
в пособии. Задания по переводу с русского языка на английский 
направлены на повторение и закрепление терминологии по специальности, на использование необходимого грамматического аппара-
та. Задания на прочтение математических формул позволят студентам 
получить 
достаточный 
навык 
изложения 
материала, 
содержащего математический аппарат, на английском языке. Грамматические упражнения направлены на повторение наиболее сложных конструкций английского языка. 
Владение терминологией по изучаемой специальности и языковыми оборотами английского языка, навыки понимания и перевода оригинальной литературы позволят студентам легче ориентироваться в потоке публикаций по специальности на английском 
языке, определять степень важности получаемой информации для 
собственной сферы деятельности, принимать участие в обсуждении профессиональных вопросов с зарубежными коллегами. 

Unit 1 

Texts: 
A. Pure and Applied Mathematics 
B. Why is the World Mathematical? 
C. Mathematics and Physics 
D. Revolution in Mathematics 
E. “Queen of Sciences” 
F. Experimental Mathematics 

Preliminary exercises 

I. Translate the following words and determine what part of 
speech they are. Explain your opinion. Find them in the text: 
National, international, nation, nationality, nationalism, nationalist, nationally; 
discuss, discusser, discussible, discussion; 
approximately, approximation, approximate; 
solve, solvent, solvable, solver; 
application, applicator, applicant, apply, appliancy, applicability, applied, appliance;  
extremely, extreme, extremeness, extremism, extremist, extremity;  
intractable, tract, tractable, tractate;  
essential, essence, essentially, essay; 
heavily, heavy, heaviness;  
mathematicians, mathematics, mathematical, math;  
probabilists, probable, probability;  
correctly, correct, correction, incorrect, incorrectly, correctness; 
joining, join, joint, jointless, jointly, joined;  
partition, part, particle, partial, partner, partly;  
loft, loftiness, loftily, lofty. 

II. Read Text A and find equivalent phrases in the right-hand 
column. Find them in the text: 
1) строгость и доказательства 
a) solvable problem 

2) начальные и граничные значения 
b) sloppy crackpot 

3) теоретическая и прикладная 
математика отдаляются друг 
от друга 

c) to immerse oneself completely in the subject 

4) глубокое понимание предмета 
d) joining of hands of people 
5) индуктивный метод 
e) initial and boundary values 

6) разрешимая задача 
f) living and breathing the subject 
7) полностью погрузиться в тему g) pure and applied mathematics 
are drifting apart 
8) необходимые качества 
h) inductive method 
9) объединенные усилия людей 
i) rigor and proofs 
10) неграмотный чудак 
j) requisite qualities 

III. Memorize the following basic vocabulary and terminology to 
Text A: 
pure mathematics — чистая математика 
applied mathematics — прикладная математика 
boundary value — граничное значение 
boundary value problem — краевая задача 
approximate solution — приближённое решение 
exact problem — строгая задача 
solvable problem — разрешимая задача 
intractable problem — трудноразрешимая задача 
initial value problem — задача Коши, задача с начальными условиями 
recognize the need — признавать необходимость 

Text A 

Pure and Applied Mathematics 

Toward the end of the recent International Congress of Mathematicians 
in Madrid, there was a discussion about whether pure and applied 
mathematics are drifting apart. The majority of the audience was pure 
mathematicians. So perhaps it would be helpful to ask, what is applied 
mathematics?  
A very good answer was provided by Kurt Friedrichs, who distinguished himself in both pure and applied mathematics, “Applied math

ematics consists in solving exact problems approximately and approximate problems exactly.” Initial and boundary value problems associated 
with the Navier-Stokes equations are an example of problems that are 
extremely difficult to solve exactly and where approximate solutions 
are looked for. Hence computing is an important part of applied mathematics. The Bhatnagar Gross-Krook equation in kinetic theory and 
plasma physics is an example of a solvable problem that approximates 
an intractable one. 
Some mathematicians believe that pure mathematics is a branch  
of applied mathematics. Some of the greatest mathematicians of the 
past — Newton, Euler, Lagrange, Gauss, and Riemann — and more recently Hilbert, Weyl, Wiener, von Neumann, and Kolmogorov did both 
pure and applied mathematics.  
There was the opinion that proofs are essential in pure math, but 
they are essential in applied math too, except that the path one takes is 
rather different. Applied math relies heavily on the inductive method, 
as opposed to the deductive method preferred by pure mathematicians. 
In pure mathematics the emphasis is on rigor. However, ideas are far 
more important. Ideas come from intuition, of course, which in turn 
comes from living and breathing the subject. Some of the scientists are 
quite right in insisting that even applied mathematicians need basic 
training in mathematics. One must also immerse oneself completely in 
the subject to which one wants to apply mathematics.  
It is by gaining a thorough understanding of the problems arising in 
the subject one develops a feeling for it, and with it, intuition. In applied mathematics the emphasis on rigor and proof must come at the 
appropriate stage. Let us consider an example. Feynman had great intuition but didn’t care much for rigor or proofs. He says in one of his 
autobiographical writings that once he used to talk to William Feller 
and Mark Kac, the famous probabilists. It is a happy circumstance, for 
science in general and mathematics in particular, that Feller and Kac 
didn’t dismiss Feynman as a sloppy crackpot but instead patiently listened to him. Thus the great Feynman-Kac formula was born. The moral, I think, is that pure mathematicians, while insisting correctly on rigor and proofs, must be patient and show some respect toward intuition 
born out of a deep knowledge of a subject. Attitudes like “Applied 
mathematics is bad mathematics” are shortsighted. For their part, applied mathematicians, while using intuition as their guide, must recognize the need for and the importance of proofs. On the other hand, it is 

rare that a single individual embodies all the requisite qualities to a high 
degree. So often what is needed is a joining of hands of people with 
disparate abilities, strengths, and points of view rather than a separation 
or drifting apart.  
(3 253) 

Task 1. Answer the following questions. 
1. What was one of the questions discussed at the recent International 
Congress of Mathematicians in Madrid? 
2. How did Kurt Friedrichs define the difference between pure and applied mathematics? What example could prove his point? 
3. What does applied mathematics require besides basic training in 
mathematics? 
4. Thanks to what circumstances was the famous Fayman-Kac formula 
born? What is proved by that fact? 
5. What is the source of intuition? 
6. Why is the joining of hands of all mathematicians necessary in dealing with problems of mathematics?  

Task 2. Translate the following sentences into English. 
1. Прикладная математика состоит в приближенном решении точных задач и точном решении приближенных. 2. Существует мнение, что доказательства очень важны в теоретической математике. 
3. Только в результате глубокого понимания проблем, возникающих при рассмотрении конкретной темы, у человека развивается 
его тонкое восприятие, и с ним, интуиция. 4. Те, кто, занимаясь 
прикладной математикой, руководствуется интуицией, должны  
в то же время осознавать необходимость доказательств и их важность. 

Task 3. Read the following expressions, consulting the SUPPLEMENT. 

1 3
8 ; 0.12; 9.43. 

2x2 + 7x = 0; 
5
10a
 
 – 3 = 2; 2x + 3 = 
20
9
x 
; 3
2
2
11x

 = 3 + x;  

K = 
2

1

1
2

T
 R
N
R


, 

4
4

2
2

 
a – b
a – b  = 
2
a  + 
2
b . 

log m N  = logN
m
; 2sin α cos β = sin (α + β) + sin (α – β);  

3
5
dx

x


; 
2
2
a

a
a – x


 dx; 
2

2

sin
cos
1

π
x dx
x   



. 

Grammar Revision 

Grammar task 1. Find the passive constructions in Text A and 
explain them. 
Grammar task 2. Translate the following sentences into Russian 
paying attention to the passive constructions. 
1. The question of the laws of resistance in circuits may now be turned to. 
2. Many materials now commonly used were not even thought of forty 
years ago.  
3. This result was aimed at. 
4. Mathematics, astronomy and physics were the first sciences to get 
organized and defined. 
5. The speed with which arithmetic operations are performed is affected 
by a number of factors. 
6. Questions can be asked and answered, but unfortunately the questions asked and those answered are frequently not the same. 
7. These problems were being discussed by physicists for many years. 
8. The equipment was sent for. 
9. The force was acted upon. 
10. Advantage was taken of this fact. 
11. Use is being made of the new technique developed by the young 
engineer. 
12. Care should be taken of the exact following the instructions. 
13. This question was very important but not paid due attention to. 
14. The weak points in the thesis were not taken notice of. 
15. The young man left the city and was lost sight of. 
16. Materials can be classed in three groups according to their electrical 
properties — conductors, semiconductors and insulators. 
17. The results of the Dubna physicist research work are made good use of 
in such fields as biology, medicine, geology and science of metals.  

18. An atom of any substance may be represented by a central core 
having a positive charge and surrounded by orbiting electrons, each 
having a negative charge. 
19. Granules cannot be obtained from such metals. 
20. The book was terribly bad; it was just a chance that it got published. 

Supplementary reading tasks 

Read and translate Text B without a dictionary 

Text B 

Why is the World Mathematical? 

This reflection on the symmetries behind the laws of nature also tells us 
why mathematics is so useful in practice. Mathematics is simply the 
catalogue of all possible patterns. Some of those patterns are especially 
attractive and are studied or used for decorative purposes; others are 
patterns in time or in chains of logic. Some are described solely in abstract terms, while others can be drawn on paper or carved in stone. 
Viewed in this way, it is inevitable that the world is described by mathematics. We could not exist in a universe in which there was neither 
pattern nor order. The description of that order (and all the other sorts 
that we can imagine) is what we call mathematics. Yet, although the 
fact that mathematics describes the world is not a mystery, the exceptional utility of mathematics is. It could have been that the patterns behind the world were of such complexity that no simple algorithms could 
approximate them. Such a universe would “be” mathematical, but we 
would not find mathematics terribly useful. We could prove “existence” 
theorems about what structures exist, but we would be unable to predict 
the future using mathematics in the way that NASA’s mission control 
does.  
Seen in this light, we recognize that the great mystery about mathematics and the world is that such simple mathematics is so farreaching. Very simple patterns, described by mathematics that is easily 
within our grasp, allow us to explain and understand a huge part of the 
universe and the happenings within it. 
(1520) 

Read Text C and give a short summary. 

Text C 

Mathematics and Physics 

The traditional view is that mathematics and physics are quite different. 
Physics describes the universe and depends on experiment and observation. The particular laws that govern our universe — whether Newton’s 
laws of motion or the Standard Model of particle physics — must be 
determined empirically and then asserted like axioms that cannot be 
logically proved, merely verified. Mathematics, in contrast, is somehow 
independent of the universe. Results and theorems, such as the properties of the integers and real numbers, do not depend in any way on the 
particular nature of reality in which we find ourselves. Mathematical 
truths would be true in any universe. Yet both fields are similar. In 
physics and indeed in science generally, scientists compress their experimental observations into scientific laws. They then show how their 
observations can be deduced from these laws. In mathematics, too, 
something like this happens — mathematicians compress their computational experiments into mathematical axioms, and they then show 
how to deduce theorems from these axioms. If Hilbert had been right, 
mathematics would be a closed system, without room for new ideas. 
There would be a static, closed theory of everything for all of mathematics, and this would be like a dictatorship. In fact, for mathematics to 
progress you actually need new ideas and plenty of room for creativity. 
It does not suffice to grind away, mechanically deducing all the possible consequences of a fixed number of basic principles. An open system is much more preferable. Rigid, authoritarian ways of thinking are 
ineffective. Another person who thought mathematics is like physics 
was Imre Lakatos, who left Hungary in 1956 and later worked on philosophy of science in England. There Lakatos came up with a great 
word, “quasiempirical,” which means that even though there are no true 
experiments that can be carried out in mathematics, something similar 
does take place. For example, the Goldbach conjecture states that any 
even number greater than 2 can be expressed as the sum of two prime 
numbers. This conjecture was arrived at experimentally, by noting empirically that it was true for every even number that anyone cared to examine. The conjecture has not yet been proved, but it has been verified